The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space
Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 2, p. 199-215
@article{AIHPA_1999__71_2_199_0,
     author = {Nakamura, M. and Ozawa, Tohru},
     title = {The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {71},
     number = {2},
     year = {1999},
     pages = {199-215},
     zbl = {0960.35066},
     mrnumber = {1705131},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1999__71_2_199_0}
}
Nakamura, M.; Ozawa, T. The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space. Annales de l'I.H.P. Physique théorique, Volume 71 (1999) no. 2, pp. 199-215. http://www.numdam.org/item/AIHPA_1999__71_2_199_0/

[1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976. | MR 482275

[2] P. Brenner, On Lp-Lp' estimates for the wave equation, Math. Z. 145 (1975) 251-254. | MR 387819 | Zbl 0321.35052

[3] T. Cazenave and F.B. Weissler, The Cauchy problem for the critical nonlinear Schrödinger equation in HS, Nonlinear Anal. TMA 14 (1990) 807-836. | MR 1055532 | Zbl 0706.35127

[4] V. Georgiev and P.P. Schirmer, Global existence of low regularity solutions of non-linear wave equations, Math. Z. 219 (1995) 1-19. | MR 1340845 | Zbl 0824.35074

[5] J. Ginibre, Scattering theory in the energy space for a class of nonlinear wave equation, Adv. Stud. Pure Math. 23 (1994) 83-103. | MR 1275396 | Zbl 0827.35077

[6] J. Ginibre, T. Ozawa and G. Velo, On the existence of the wave operators for a class of nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique théorique 60 (1994) 211-239. | Numdam | MR 1270296 | Zbl 0808.35136

[7] J. Ginibre, A. Soffer and G. Velo, The global Cauchy problem for the critical non-linear wave equation, J. Funct. Anal. 110 (1992) 96-130. | MR 1190421 | Zbl 0813.35054

[8] J. Ginibre and G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985) 487-505. | MR 786279 | Zbl 0549.35108

[9] J. Ginibre and G. Velo, Regularity of solutions of critical and subcritical nonlinear wave equations, Nonlinear Anal. 22 (1) (1994) 1-19. | MR 1256167 | Zbl 0831.35108

[10] J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995) 50-68. | MR 1351643 | Zbl 0849.35064

[11] L.V. Kapitanski, Weak and yet weaker solutions of semilinear wave equations, Comm. Partial Differential Equations 19 (1994) 1629-1676. | MR 1294474 | Zbl 0831.35109

[12] L.V. Kapitanski, Global and unique weak solutions of nonlinear wave equations, Math. Res. Lett. 1 (1994) 211-223. | MR 1266760 | Zbl 0841.35067

[13] H. Lindblad, Global solutions of nonlinear wave equations, Comm. Pure Appl. Math. XLV (1992) 1063-1096. | MR 1177476 | Zbl 0840.35065

[14] H. Lindblad, A sharp counterexample to the lacal existence of low-regularity solutions to nonlinear wave equations, Duke Math. J. 72 (1993) 503-539. | MR 1248683 | Zbl 0797.35123

[15] H. Lindblad and C.D. Sogge, On existince and scattering with minimal regularity for semilinear wave equations, J. Funct. Anal. 130 (1995) 357-426. | MR 1335386 | Zbl 0846.35085

[16] M. Nakamura and T. Ozawa, Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Rev. Math. Phys. 9 (3) (1997) 397- 410. | MR 1446653 | Zbl 0876.35080

[17] M. Nakamura and T. Ozawa, The Cauchy problem for nonlinear wave equations in the Sobolev space of critical order, Preprint.

[18] H. Pecher, Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichumgen, I, Math. Z. 150 (1976) 159-183. | MR 435604 | Zbl 0318.35054

[19] H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equation, Math. Z. 185 (1984) 261-270. | MR 731347 | Zbl 0538.35063

[20] H. Pecher, Local solutions of semilinear wave equations in Hs+1, Math. Methods Appl. Sci. 19 (1996) 145-170. | MR 1368792 | Zbl 0845.35069

[21] R.S. Strichartz, Convolution with kernels having singularities on a sphere, Trans. AMS 148 (1970) 461-471. | MR 256219 | Zbl 0199.17502

[22] R.S. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal. 5 (1970) 218-235. | MR 257581 | Zbl 0189.40701

[23] R.S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977) 705-714. | MR 512086 | Zbl 0372.35001

[24] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983. | Zbl 0546.46027